|
, .as when the stakes can be varied--always assuming that as many players would come to them, and play as freely, as on the present more attractive system.
Let us consider the actual state of the case, when a player at a table doubles his stakes till he wins--repeating the process from the lowest stakes after each Success.
But first--or rather, as a part of this inquiry--let us consider why our imaginary player B would decline to allow A to double wagers in the manner described. In reality, of course, A's power of doubling is limited by the amount of A's money, or of his available money for gambling. He cannot go on doubling the stakes when he has paid away more than half his money. Suppose, for instance, he has 1,000l. in notes and 30/. or so in sovereigns. He can wager successively (if he loses so often) 1l., 21., 41, 81., 161., 321., 641., 128l., 256l., 512l., or ten times. But if he loses his last wager he will have paid away 1,028l., and must stop for the time, leaving B the gainer of that sum. This is a very unlikely result for a single trial. It would not be
likely to happen in a hundred or in two hundred trials, though it might happen at the first trial, or at a very early one. Even if it happened after five hundred trials, A would only have won 500/. in those, and 13 winning 1,023l. at the last, would have much the better of the encounter. Why, then, would not B be willing to wager on these terms ? For precisely the same reason (if he actually reasoned the matter out) that he should be unwilling to pay Il. for one ticket out of 1,024 where the prize was 1,024l. Each ticket would be fairly worth that sum. And many foolish persons, as we know, are willing to pay in that way for a ticket in a lottery, even paying more than the correct value, rut no one of any sense would throw away a sovereign for the chance (even truly valued at a sovereign) of winning a thousand pounds. That, really, is what 13 declines to do. Every venture he makes with A (supposing A to have about 1,000/.at starting, and so to be able to keep on doubling up to al2l.) is a wager on just such terms. B wins nothing unless he wins 1,024l.; he loses at each failure 1l. His chance of winning, too, is the same, at each venture, as that of drawing a single marked ticket from a bag containing 1,024 tickets. Each venture, though it may be decided at the first or second tossing, is a venture of ten tossings. Now, with ten tossings there are 1,024 possible results, any one of which is as likely as any other. One of these, and one only, is
Thus he pays, in effect, one pound for one chance in 1,024 of winning 1,024l., though, in reality, he does not pay the pound until the venture is decided against him; so that, if he wins, he receives 1,023/., corresponding (with the 11.) to the total just named.
|
